On Triangular Representations of Aut(Fr)

If ρ: Fr → GLn(K) is a representation of a finitely generated free group Fr, and ρ(a)m = I for each basic element (i.e., element which occurs in some basis) a, then we show that if ρ(Fr) is triangularisable, it is finite. This can be thought of as a generalisation of the Burnside problem for these linear groups.